It was decided to title this paper "The chaotic house of primes and the unprovable Riemann hypothesis" since the aim is to photograph the structure in which the prime numbers are placed (the house), to analyse the results obtained in the context of the Riemann hypothesis, results that attest to its non-verifiability, and finally to put emphasis on the distribution of primes, a distribution that is not random, not regular, but chaotic and from which order is generated. Taking advantage the complementarity of the set of prime numbers with that of composite numbers, it is possible to photograph the structure in which primes are placed using the ordered structure of composite numbers. The latter is described by two families of double sequences (x,y) defined in Z_(x>l; y>m)^2→N_(>8) and whose analytical expressions change according to the choice of parameters l,m∈Z. Graphical representations follow to better grasp the regularity of composite numbers, as well as the spaces left by them free where the prime numbers find "house". It is therefore possible to shed light on the distribution of primes and at the same time validate and contradict a particular aspect of the Riemann, namely that prime numbers are distributed with regularity. It follows the thesis according to which the Riemann hypothesis is impossible to prove or to disprove due to the "falsely ordered" nature of prime numbers. In fact, their nature is neither ordered nor random, but chaotic and generative of the order, the true one of composite numbers which, due to their complementarity with prime numbers, make appear ordered even the prime numbers. These are the conclusions.